The common currency of energy ex- change in living things is the hydrolysis of adenosine tri- phosphate ATP to adenosine diphosphate ADP and orthophosphate Pi or to adenosine monophosphate AMP and pyrophosphate PPi (1, 9). The purpose of this article is to discuss certain aspects of the thermo- dynamics of the first reaction.

ATP + HQO = ADP + Pi (1)

Robert A. Alberty Massachusetts Institute

of Technology Cambridge, 02139

The observed equilibrium constant Kobe, which is usu- ally used by biochemists, is defined by

Thermodynamics of the Hydrolysis of Adenosine Triphosphate

where [ATP] represents the total molar concentration of ATP including all the ionized and complexed forms.

This type of equilibrium constant is convenient for use in the laboratory because the experimenter is interested in the relation between the equilibrium concentrations of ATP, ADP, and Pi in dilute solutions when the pH and electrolyte concentrations in the aqueous solution are held constant. The value of Kobe is also of interest because it can be used to calculate the amount of work (excluding PAT' work) which can be obtained in prin- ciple when a mole of ATP is hydrolyzed a t constant temperature and pressure. The hydrolysis of one mole of ATP under physiological conditions can yield as much as 5-10 kcal of work (that is, this is the value of -AGob., the decrease in Gibbs free energy), but the amount of work actually obtained depends on how this reaction is coupled with others. Since the maximum amount of work depends upon the pH and concentra- tions of metal ions, as well as the temperature, it is of interest to see how big these effects are and what causes them.

Specifically we will be interested in the following types of questions: If Koba is known a t one pH and metal ion concentration, what is its value a t another pH and in the presence of another metal ion or a different metal ion concentration? If the heat evolved at constant tem- perature and pressure (AH, the enthalpy change) is determined at one pH and metal ion concentration, what will be the heat evolution under another set of conditions? Since the reaction may produce or con- sume H+ and metal ions, what is the stoichiometry under various conditions? What are the relative con- tributions of enthalpy and entropy change to the change in standard Gibbs free energy for the reaction?

It will probably come as a surprise to you that Kob. is a function of pH and metal ion concentrations, even a t constant temperature, pressure, and total electrolyte concentration. This is a result of the way Kobe is de- fined in eqn. (2). Since Koba deals with sums of ionized and complexed species, we will find that the thermo-

dynamic quantities consist of sums of terms and that these various contributions vary with pH and metal ion concentration. The basic ideas have been discussed in a number of recent articles (5-5).

Theory

The hydrolysis of ATP may be expressed in terms of particular ionized species

ATP" + HzO = ADPa- + H P O P + H+ (3)

The corresponding equilibrium constant expression is

The hydrolysis of ATP could equally well be expressed in terms of other ionized species, but we will stick with eqn. (4) (which is also K, in the table) throughout this article. Since the choice of components is arbitrary in thermodynamics, we may calculate the Gibbs free energy of hydrolysis and other thermodynamic quanti- ties using either Koba [eqn. (2) I or Ki [eqn. (4) 1.

Comparison of these two points of view provides some excellent illustrations of elementary chemical thermo- dynamics. If all the known species of ATP, ADP, and P. are taken into account, the equations get a little long (5-5), and so we will consider an incomplete set of equilibria here so that the important basic principles will not be buried. To calculate the effect on reaction 1 of changing pH in the range 4-10 it is necessary to take into account two acid dissociations of ATP, two of ADP, and one of Pi, but we will ignore these ionizations and talk about effects of changing the concentration of magnesium ion at a constant pH of 9 and 25°C. Two magnesium complexes of ATP and two of ADP are known, but we will consider only the ATP complex forped at the lowest magnesium ion concentration and the ADP complex formed at the lowest magnesium ion concentration. Since the magnesium ion concentration may vary over many powers of ten, i t is convenient to use pMg = -log[Mg2+], where [MgZ+] is the mag- nesium ion concentration in moles per liter. If pMg is determined by use of a divalent cation electrode, we can think of [Mgz+] as the magnesium ion activity on the moles per liter scale.

The equilibria we will consider may be summarized as follows:

ATPa- + HIO k~ ADPa- + HP0,'- + H+ n Kl KI T ~ K I Tl Ka ( 5 )

MgATPa MgADPL- MgHPOP

The values of the equilibrium constants at 25'C and 0.2 ionic strength are summarized in the table (5). In the calculations it is assumed that there are no other cations in the electrolyte which form complexes with ATP4-,

Volume 46, Number 1 1, November 1969 / 713

Thermodynamic Parameters for lonic Reactions a t 25'C and 0.2 lonic Strength

AGO kcal AH" kcd AS' cal Constant pKa mole-' mole-' deg-1 mole-'

1. MgATP2- = Mg2+ + ATP4- K I 4.00 5.46 - 3 .3 -29.4 2. MgADP1- = Mgs+ + ADPa- I f% 3.01 4.11 -3.6 -25.9 3. MgHPOP = Mg2+ + HPOIZ- Ka 1.88 2.56 -2 .9 -18.3 4. ATP4- + HHIO = ADP3- + HP0.a- + H+ K* 0.28 - 4 . 7 -16.7 5. MgATP2- + H20 = ADP8- + HPO,%- + H+ + Mgat 5 . 7 4 - 8 . 0 -46.1 6. MgATP2- + H1O = MgADP1- + HPO2 + H+ 1.63 -4 .4 -20.2 7. Mg2+ + MgATPZ- + HnO = MgADPL- + MgHPOP + H + -0.93 -1.5 - 19

a pK = -log K, where K is expressed in terms of concentrations in moles/l.

ADPa-, and HPOa2-. This means that Na+ and I<+ must not he present. They do form complexes with ATP4- and ADP3- (6). The highly shielded cation (n-pr~pyl)~N+ has much less tendency to form complex ions with these anions than even (CH3)4N+, and so we will assume that the electrolyte is 0.2 M tetra-n-propyl ammonium chloride. I t is assumed that at constant ionic strength the activity coefficients are constant so that equilibrium expressions may simply be written in terms of concentrations. This actually means that we assume the solutions of the various ions in the elec- trolyte to be ideal; that is, the chemical potential p of ATP4-, for example, is given by p = po + RT In [ATP4-1, for very small ATP4- concentrations. We assume that A T P 4 makes only a small contribution to the constant ionic strength of 0.2; in other words we are concerned with solutions in which [ATP4-] << 0.2/16.

I t is of interest to consider why the dissociation constants for MgATP2-, MgADP1-, and h4gHP040 have the values they do. The pK values show that ATP4- is half saturated with Mg2+ when [Mg2+] = lO-'.QQ M; ADPa- is half saturated with Mg2+ when [Mg2+] = M; and HPOn2- is half saturated with Mgz+ when [Mg2+] = 10-1.88 M. In each case the enthalpy change favors dissociation, but the stan- dard entropy change opposes dissociation and also reac- tions 4-7. Now are the standard entropy changes ASo reasonable? When a complex ion dissociates, it might he expected that there would be an increase in entropy because the two product ions might be expected to have more degrees of freedom than the complex ion, so that the final state could be considered to be more "random" than the initial state. However, in each of these cases the ASo is negative so that according to the "random- ness" interpretation of entropy the complex ion must he more "random" than the ions into which it dissociates. This remarkable result is a consequence of the unusual properties of water as a solvent. Since a water molecule has a dipole moment it tends to be oriented in the inhomogeueous electric field surrounding an ion. We speak of the ions as being hydrated and of the more highly charged ions as being more hydrated, but we do not know enough about the effects of ions on the structure of water to describe this "hydration" very accurately. Nevertheless it seems clear that the de- crease in entropy upon dissociation of the complex ion results from an increased orientation of water in the final (dissociated) state. Thus in all three cases the standard entropy change is unfavorable for dissociation; the final (dissociated) state is a more ordered state. This entropy effect is biggest for the most highly charged anion and so MgATP2- has less tendency to dissociate than MgADPl-, which has less tendency to dissociate than MgHPOI0.

The observed equilibrium constant defined by eqn. (2) is expressed in terms of the ion concentrations by

where the last form is obtained by introducing eqn. (4). The dependence of log Kobs on pMg is shown in Figure 1. The slope of this plot gives the number nm. of moles of MgZ+ liberated per mole of ATP hydrolyzed (7). It may come as a surprise to you that Mg2+ may be con- sumed or liberated by reaction 1 since we have not in- cluded this possibility in the "balanced" chemical equa- tion. The reason it is not included in eqn. (1) is that generally the experimentalist does not measure nu.. At a given pMg and pH the value of n ~ , is constant, and the fact that it is omitted in eqns. (1) and (2) does not limit the usefulness of Kobs, provided we remember it is a function of pH and metal ion concentration. The value of nn, may he calculated from the following equa- tion (3).

This derivative may be evaluated by taking the deriva- tives d log K,b./d[Mg2+] and d pMg/d[Mg2+] and tak- ing the ratio. This leads to

The meanings of these terms are easily seen. The first is the average number of Mg2+ bound per mole of ATP, the second is the average number of MgZ+ bound per mole of ADP, and the third is the average number bound per mole of orthophosphate.

The variation of n ~ . with pMg which is shown in Figure l b may be interpreted in terms of reactions 4-7 in the table. At sufficiently low magnesium ion concen- trations this ion is not bound by any of the reactants or products and nm. = 0. Reaction 4 predominates. As the magnesium ion concentration is raised to about

M, the binding of Mg'+ by ATP4- becomes significant and reaction 5 becomes important. For reaction 5, nm. = 1, but before this value can be reached reaction 6 becomes important, and n ~ , begins to approach the value for this reaction nu. = 0. As pMg approaches 2 the binding of Mg2+ by HPO? be- comes important and nm, changes toward -1, which is the value for reaction 7.

The effect of pMg on Kobe is a good example of Le

714 / Journd of Chemical Education

-0.5 L 2 3 4 5

_1 6

PMQ

Figure 1. o, Log KOb, for reaction 1 a t 25'C and pH 9 in 0.2 ionic strenglh 0% o function of pMg, colculated with eqn (61. b, Number

nu. of moles of MgZc liberated by reaction 1, colculated with eqn. 181.

Chatelier's principle. If nnr, is positive as i t is in the pMg range of approximately 2.5-5, raising [Mg2+], that is lowering pMg, pushes the reaction backward. Thus at successively lower values of pMg in this range, Koba has successively lower values. However, at pMg < 2.3, n ~ , is negative (that is, MgZ+ is used up by the reaction) and lowering pMg (raising the concentration of mag- nesium ions) pushes the reaction to the right. That is, Kohl is increased by raising [Mgz+] in this range. It will be interesting to find out how nature uses control mechanisms of this type to regulate chemical reactions in the cell.

Calculation of Thermodynamic Quantities for ATP Hydrolysis

The expression of KDbs in terms of equilibrium con- stants and concentrations is the key to the calculation of the standard Gibbs free energy change AGoob., the standard enthalpy change AHoOb., and the standard entropy change ASo.b.. AGS,ba = -RT In Koba (9)

The change in standard Gibbs free energy AGo,s. is equal to the molar Gihbs free energy of ADP in hypo- thetical one molar aqueous solution plus that of hypo- thetical one molar orthophosphate minus that of hypo- thetical one molar ATP all a t 25'C in 0.2 ionic strength tetra-n-propyl ammonium chloride. The dependence of AGOob. on pMg is given in Figure 2. It is important to understand that the 0.28 kcal mole-' shown for reac- tion 4 in the table is the change in standard Gibbs free energy AGO for the conversion of hypothetical one molar ATP4- to hypothetical one molar ADP3-, hypothetical one molar DO4-1, and unit activity H+ at 25'C in 0.2 ionic strength tetra-n-propyl ammonium chloride.

-TASaoa.

-8 ;k 2 3

4 5 6 PMQ

Figure 2. a, Standard Gibbr free energy change AGOah. in ksol mole-' for reaction 1 mt 2.5-C and pH 9 in 0.2 ionic strength electrolyte, calculated with oqnr. 161 and 191 (or 361. b, Standard entholpy chonge AH',b, in kcol molec' ealcvloted with eqn. 11 21. This is the heat evolved when the reoction iscarried out atconstant temperature m d pressure. c, - TASO.,br in kcel mole-1 rolculated using eqn. (1 41 or 1301, where ASDOh. is the rtanderd entropy change for reoction 1. The rum d the ordinates of the two lower plots giver the ordinate of the upper plot.

The heat of hydrolysis of ATP a t constant tempera- ture and piessure is given by AHo,,.. Since AHo of reaction 4 in the table and the enthalpies of dissociation of the complex ions R4gATP2-, MgADP1-, and MgHPOP are known, the effect on the heat of hydroly- sis by changing pMg may be calculated. When we differentiate in Koba with respect to T according to eqn. (10) we obtain

b In Kob. = RTI 3 In Kt Wg2+l/Ka AHDOb. = RT2- 3T bT 1 + [Mg2+l/Kt b In K2 - [MgP+l/Ks R ~ l X RTZ-

bT 1 + [Mga+l/Ks 3T b In K1 [Mg2+l/Kt RTe

+ 1 + [Mg2+l/K, bT

lMgz+l/Ka - [Mg'+l/Ks AH1O

= AH'o - 1 + [Mge+]/Kn 1 + IMg'+l/Ka [MgZtl/Kt AH,D (12)

+ 1 + [MgH1/K,

where the second form is obtained by substituting the corresponding AH0 (given in the table) for RT2 Mn K/bT. I t can be seen that AHoOb. is a kind of weighted average AHo, and we will in fact refer to it later as AHo.,. In the absence of Mg2+, AHoOb. = AHlo = -4.7 kcal mole-I (8-10). As the concentration of magnesium ions is increased AHaOb. drops toward -8.0 kcal mole-', the enthalpy change for reaction 5 in the table. But before this reaction predominates, reaction 6 becomes important and the plot of AHooba rises. AS the magnesium ion concentration is raised in the vicinity of pMg 2, AHoOb. rises toward -1.5 kcal mole-', the value for reaction 7. However, the limiting values given for reactions 5; 6, and 7 in the table are never reached because these reactions do not really pre- dominate in any range of pMg.

We are now in a position to calculate ASo.b. using eqn. ( 1 1 ) or

Volume 46, Number 1 I, November 1969 / 715

Either way we obtain

+ R ln (1 + lMga+l/Kd + R In (1 + [Mg2+l/Kd - R In [Ht] - R In (1 + [Mg'+]/K>) (14)

The values of -TASo,b , are given in Figure 2. It is convenient to give the entropy changes in this form so that the sum of the ordinates of the two lower plots gives the ordinate of the upper plot. The sign of the standard entropy change ASoOb, is favorable for hydrolysis of ATP at all values of pMg; that is, ASo.b, is positive. In fact the entropy change contributes more to the negative value of AGOob. than does AHooba, except in the vicinity of pMg 3.5. It is of interest to note how the relative contributions of AHoOh, and ASooba shift with changing pMg.

Interpretation of ASoab.

To be sure eqn. (14) yields ASaoba, but it is disappoint- ing that we cannot see in i t anything familiar or interest- ing. Perhaps the equation can he rearranged into a more meaningful form. King (1 1) has pointed out that when thermodynamic quantities are measured for a composite reaction, the entropy of mixing of the related species of reactants and products come into the equation for the standard entropy change of the composite reac- tion. Since the products and reactants in reaction 1 exist in multiple forms, we should expect to find mixing terms in eqn. (14). The entropy of mixing the two forms of ATP fATP4- and MgATP2-) is

This is the entropy of mixing 1/(1 + [Mg2+]/K,) moles of ATP4- with ([Mg2+1/KJ/(1 + [Mg2+l/K~) moles of MeATP2- to form an ideal mixture. Since the - ~-~~ ~ - logarithms of the mole fractions are negative, ASo,i,mp is positive. Since AHo for mixing of ideal solutions to form an ideal solution is zero, AGO is negative and the mixing is a thermodynamically spontaneous process at constant temperature and pressure. The standard entropies of mixing the two species of ADP and the two species of Pi are correspondingly

Now the question is whether or not we can rearrange eqn. (14) so that it shows the combinations of terms given in the preceding three equations. In eqn. (14) we have a term Rln [I + [Mg2+]/K2]. What has to he done to this term to get the combination of terms defined as AS",i,ADp given in eqn. (16)? First we invert the

quantity in the logarithm and multiply and divide by 1 + [Mg2+l/Kz.

1 + lMga+l/Kl 1 R l n l l + IMga+l/KJ = -R + [Mgl+]/Kn 1 + [ M ~ ~ + ] / K ,

If we only had a term

we would have ASomidop; SO let's add and subtract this term from eqn. (18). Thus eqn. (18) may he written

R ln[l + [MgW]/Kzl = ASomir*m

Similarly R lnll + IMaP+l/Ktl = AS",~,ATF

Substituting these three equations into eqn. (14) and doing a little rearranging yields

= AS',,. + AS0,i.mp + A S o m i r ~ - A S D m i x ~ ~ ~ - R In [Hf1 - Rnu. In [Mg2+l (22)

where nM,, the number of moles of magnesium ion pro- duced, is given by eqn. (8) and

which is of the same form as eqn. (12). If one ionic reaction predominates these four terms simply yield ASo of the predominating ionic reaction.

Thus AS0.& contains the weighted average of the first four standard entropy changes from the table, and the three expected entropies of mixing, hut what are the lmt two terms? They must he related to the fact that the hydrolysis of ATP at pH 9 produces one mole of H+ and n ~ , moles of Mg2+ per mole of ATP hydrolyzed. The last two terms in eqn. (22) are entropy of dilution terms. Before going on to discuss them it is worth not- ing how helpful algebra is in rearranging an equation which doesn't seem to have any meaning (eqn. (14)) into one that is full of meaning (eqn. (22)).

716 / lournol of Chemicol Educofion

Entropy of Dilution

The entropy of expansion of one mole of an ideal gas from volume Vl (and concentraion CI = ~ / V I ) to volume V2 (and concentration cz = l/Vz) is given by (19)

This equation may also be applied to the dilution of a component of an ideal solution. If the intial concentra- tion is 1 M

AS = -R in cs (25)

Thus for the dilution of a mole of H + from 1 M to [H+] = 10-vH M

ASodil.x = -R In [HC] = -2.3Rlog 10-pH = 2.3 R(pH) (26)

Similarly for the dilution of n ~ . moles of Mg2+ from 1 M to [MgZ+] = 10W'"gM.

ASod,l.arg = -nx. R in [Mga+] = 2.3 n u . R(pMg) (27)

In order to understand how these entropy of dilution terms arise, we can imagine reaction 1 as taking place in steps with H+ and R!gZ+ being produced a t 1 M. Then the H + and Mg2+ ions produced must be diluted from 1 M to 10-pH and 10-pMg M. These dilution processes may give rise to a considerable increase in entropy and may contribute significantly to making the over-all reaction spontaneous. Thus the Gihbs free energy of hydrolysis of ATP is more due to dilution of the H+ pro- duced than to a change in enthalpy.

Figure 3. a, Weighted overage stondord Gibbs free energy chong* AGO., in kcd mole-1 calruloted with eqn. 137). b. Weighted average rtondard entholpy change AH'.,. in kcal moleCL calculated with eqn. (1 21. This is identical with AHoOb, because in ideal solutions there ore no en- thdpio% of mixing and dilution. c, -TAS0., in kcal mole-',where ASosr. is the weighted overage stmdord entropy chmnge calculated using eqn. (231.

Dilution is a spontaneons process in ideal solutions because AH = 0 and so

AG5il.n = -2.3 RT(pH) (28)

AGodilnM. = -2.3 nM. RT(pMg) (29)

If n ~ . is positive (Mg" is produced), AG,il.~Eg is nega- tive as required for a spontaneous process a t constant temperature and pressure.

Now we may rewrite eqn. (22) in the form

where

The weighted average standard entropy change ASo.,. is plotted in Figure 3c. The values of ASomi, and its three component parts are plotted in Figure 4a. The Mg2+ dilution term is plotted in Figure 4b, and the H + dilution term is simply equal to 2.3 (1.987) (9) = 41.2 cal deg-' mole-' since the pH is held constant a t 9. The entropy of dilution of Mg2+ is positive and hence makes a contribution to causing ATP to hydrolyze pro- vided pMg > 2.3. At higher concentrations of Mg2+, n ~ . is negative and A S W ~ M . opposes the hydrolysis of A TP . - - A .

It is interesting to note that eqn. (12) for AHoOb, does not have mixing and dilution terms because, as already noted, enthalpy changes are zero for these processes in ideal solutions.

Inlerprelation of AGo.b.

Now that AS"',b. has been expressed in terms of aver- age, mixing, and dilution terms, we need to go back to eqn. (6) and see whether it may be arranged in a form which shows these same types of terms. The Gibbs free energy of mixing of ATP4- and MgATP2- is

m9 Figur- 4. m, Plot of TASo,ir = TAS' , :~DP + TASomiXp - T A S o r n i d ~ p in ksol mole-L. The three component curver calculated with eqnr. (151- (17) are given as doshed liner. Since for ideal ~olvtionr there is no enthdpy of mixing, this graph may olro be interpreted or -AGo,i, - - A G a m i x ~ ~ ~ - AGDmirp + A G o r n i r ~ ~ p . b, Plot of TAS0dilohf. = -AGodi lnwc in kcal mole-' sdcul~ted with eqn. (271. TAS'di1.x = -AGodi lna = 12.3 kcal mole-' at pH 9 (from eqn. 12611.

Volume 46, Number 1 1 , November 1969 / 717

This is the Gibhs free energy change for the mixing of 1/[1 + [Mg2+]/K~] moles of ATP4- with [[Mg2+]/ K1]/[l + [Mg2+]/Kl] moles of MgATP2- to form an ideal mixture. Since the logarithm of a number less than unity is negative, AGomidm is always negative, and the mixing of ideal solutions is always spontaneous. Since ideal mixing does not involve a change in en- thalpy, AGOmi, = -TASo,i. as may be illustrated by comparing eqns. (15) and (33). Similarly for ADP and Pi

AGomidm = 1 1

RT [l + [Mg'+]/Kz In 1 + [Mg2+]/Kt

[Mg'+I/Kn [Mg2+1/Ks ] (34) + 1 + [ M ~ ' + ] / K z ~ ~ ~ + [Mg2+l/Kn

1 1 AGomirp = RT [l + [Mga+]/Ks In 1 + [MgPt]/Ki

LMgs+l/Ka In LMg"l/Ka ] (35) + I + [Mg2+]/Ka 1 + [Mga+1/Ka

If we rearrange eqn. (9) with eqn. (6) inserted in such a way that it contains the terms which are given in eqn. (33), (34), and (35), we obtain

AG',a. = AGO., + AG0,i. + AG"dil. (36)

where

AGO., may be considered to be made up of contribu- tions from AH",, = AHoQbs and ASo, since

Figures 3 and 4 have been designed to show the rela- tive contributions of various types of terms to AGOob. . . and ASO.b..

The variations of the weighted average thermody- namic functions shown in Figure 3 may be compared with the values of AGO. AHo. and ASo for reactions 4 to 7 in the table. At verylow cbncentrations of magnesium ion (pMg 6) the value of AGO., is essentially that of reaction 4, that is, 0.28 kcal mole-'. As the magnesium ion concentration is increased reaction 5 begins to dominate and AGO., rises. However, it does not get as large as for reaction 5 (5.74 kcal mole-') because Mg2+ forms a complex with ADP3- and as the mag- nesium ion concentration is further increased, reaction 6 (AGO = 1.63 kcal mole-') tends to dominate. As the concentration of magnesium ions is further increased, reaction 7 (AGO = -0.93 kcal mole-') tends to domi- nate and AGO., drops toward this negative value. The variation of AH", = AH0,b, with pMg has been dis- cussed in connection with Figure 2.

Discussion

The calculations given here are based on an over- simplification of the equilibria involved in the ATP

hydrolysis reaction. The acid dissociations of ATP, ADP, and Pi involved in the range of pH of interest also need to he taken into account (5-5). Also magnesium complexes MgHATP1- and MgHADPo need to be introduced for a complete treatment of the effect of changing pMg. Under particular experimental condi- tions other cations which are bound may he present (for example, Na+ and I<+). The effect of mixtures of cal- cium and magnesium salts on Kobs has been calculated (5). If only H + and Mg2+ have to be considered AGOob,, AHaOhl, and ASoOh. are functions of two variables, pH and pMg, and may be represented by surfaces above a plane with coordinates pH and pMg. The number of moles nn of H + and nnr, of Mg2+ produced are related through (18, 14)

Since at constant pressure and constant ionic medium the thermodynamic quantities are functions of pH, pMg, and T, there are more Maxwell relations than for systems having only P and T as independent variables (15).

Why does the hydrolysis of ATP go so far to the right a t pH 9? This question may be discussed in terms of eqn. (36). Since AGO,, is positive over the whole range of pMg discussed here, this must not be the answer. Incidentally the value of AGO., is independent of the choice of reaction 4 as the "base" reaction. Since AG0,,. is always less than 1 kcal mole-', this term is not decisive and may, as a matter of fact, oppose hydrolysis. I n AGodxln the term -2.3 nMg RT(pMg) is interesting but never contributes more than 2 kcal mole-' favoring hydrolysis. However, the free energy of dilution of H+ is very large (-12.3 kcal mole.-') a t pH 9 and this term, almost alone, is responsible for the large value of Kobe at pH 9.

The calculations presented here do not exhaust the subject because (1) there are experimental uncertainties in the values in the table and (2) ideal solutions have been assumed. This emphasizes the need for improved thermodynamic data on reactions like the hydrolysis of ATP so that biochemists may be provided with thermo- dynamic functions that will help them in the laboratory and will help them understand quantitatively how living things operate. Thermodynamics can provide only part of this understanding, but it does provide the framework within which kinetics and enzyme catalysis opegate.

Literature Cited

(1) LEHNINGER, A. L., "Bioenergetics," W. A. Benjamin, Inc., New York, 1965.

(2) KLOTZ, I., "Energy Changes in Biochemical Reactions," Academic Press, New York, 1967.

(3) ALBERTY, R. A., J . Bwl. Chem., 243, 1337 (1968). (4) PHILLIPS. R. C.. GEORGE. P.. AND RUTMAN. R. J.. J. Bwl. . .

~hem.,'244,3330 (1969 j. '

(5) ALBERW, R. A,, J . Biol. Chem., 244, 3290 (1969). (6) SMITH, R. M., AND ALBERTY, R. A,, J. Phya. C h a . , 60, 180

(1956). (7) GREEN, I., AND MOMMAERTS, W. F. H. M., J. Bwl. Chem.,

202, 541 (1953). (8) PODOLBKY. R. J.. AND STURTEVANT. J. M.. J. Bid. Chem.. . .

217,603 (1955j. (9) KITZINGER, C., AND BENZINGER, T., Z. Naturforsch., 106,

375 (1955).

718 / Journal of Chemical Education

(10) PODOLSKY, R. J., AND MORALES, M. F., J . B id . C h a . , John Wiley & Sons, Inc., New York, 1966, p. 78. 218, 945 (1956). (13) WYMAN, J., Aduances in Protein Chem., 4,407 (1948).

(11) KING, E. L., J. CHEM. EDUC., 43, 478 (1966). (14) WYMAN, J., Advances in Protein Chem., 19,223 (1964) (12) DANIELS, F., AND ALBERTY, R. A., "Physical Chemistry,'' (15) ALBERTY, R. A,, J . Am. Chem. Soc., 91, 3899 (1969).

+

Volume 46, Number I I , November 1969 / 719